On the Expansion of a Product Formula Related with the Drinfeld Discriminant Function Original Research Article

In this work, we study the expansion of a product functionUrelated to the Drinfeld discriminantΔ(z);Uis the analogue of the classicalη-function. The main result is the formula given in Theorem 3.1. From this formula, we derive the fact that the expansion ofUis lacunary forq>2 (Theorem 3.3) and the expansion (up to a certain bound) ofUvalid for anyq, as in [Gekeler,Invent. Math.93(1988), 667–700].